Problem: Rewrite as a simplified fraction. ${1.3\overline{6} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 136.6666...\\ 10x &= 13.6666...\end{align*}}$ Subtracting the two equations, we have: ${90x = 123}$ ${x = \dfrac{123}{90}} $ ${x = \dfrac{41}{30}} \text{or} {1 \dfrac{11}{30}}$